The given equation is a quadratic equation:

\[
x^2 + 9x - 10 = 0
\]

We can solve this using the **quadratic formula**, which is:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

For the given equation \(x^2 + 9x - 10 = 0\), the coefficients are:

- \(a = 1\)
- \(b = 9\)
- \(c = -10\)

Substitute these values into the quadratic formula:

\[
x = \frac{-9 \pm \sqrt{9^2 - 4(1)(-10)}}{2(1)}
\]

\[
x = \frac{-9 \pm \sqrt{81 + 40}}{2}
\]

\[
x = \frac{-9 \pm \sqrt{121}}{2}
\]

\[
x = \frac{-9 \pm 11}{2}
\]

Now, calculate the two possible solutions:

1. \(x = \frac{-9 + 11}{2} = \frac{2}{2} = 1\)
2. \(x = \frac{-9 - 11}{2} = \frac{-20}{2} = -10\)

Thus, the solutions are:

\[
x = 1 \quad \text{or} \quad x = -10
\]

Would you like more details or have any questions?

Here are some related questions:

1. How can you verify the solutions to a quadratic equation?
2. What are other methods to solve quadratic equations?
3. What is the discriminant, and how is it used in the quadratic formula?
4. How do you factor a quadratic equation?
5. What are real-world applications of quadratic equations?

**Tip:** Always check the discriminant (\(b^2 - 4ac\)) to know if the quadratic equation has real or complex solutions.

Learn how to solve the quadratic equation x² + 9x - 10 = 0 using the quadratic formula. This step-by-step guide breaks down key algebra concepts and is perfect for students in Grades 8-10. Discover how to apply the quadratic formula and find both real solutions.

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